A hula hoop has a radius of 19 inches. What is the length of the arc subtending 1/4 of the hoop?.

Answer:

The first four terms are:  -3, -1, 1, and 3

Step-by-step explanation:

First 4 terms are:

f(1) = 2 (1) - 5  = -3

f(2) = 2 (2) - 5  = -1

f(3) = 2 (3) - 5  = 1

f(4) = 2 (4) - 5  = 3

Ludolph van Ceulen, a Dutch mathematician, calculated an impressive 35 digits of pi during his lifetime.

1. Van Ceulen used a geometrical approach called the method of polygons to approximate the value of pi.

This method involves inscribing and circumscribing polygons around a circle, then finding the perimeters of those polygons.
2. As the number of sides of the polygons increases, the perimeters of the inscribed and circumscribed polygons get closer and closer to the circumference of the circle.

The ratio of the circumference to the diameter of the circle is pi.
3. To improve the accuracy of his approximation, Van Ceulen increased the number of sides of the polygons.

He started with a polygon with a smaller number of sides and then successively doubled the number of sides.
4. For each set of polygons, Van Ceulen calculated the perimeters using trigonometric formulas and algebraic manipulations.

This process is quite labor-intensive and time-consuming, especially considering the mathematical tools available at the time.
5. By comparing the perimeters of the inscribed and circumscribed polygons, Van Ceulen was able to narrow down the range of possible values for pi.
6. Eventually, he reached a point where the polygons had so many sides that their perimeters were almost indistinguishable from the circumference of the circle.

At this stage, he determined pi to an accuracy of 35 digits.
It's important to note that Van Ceulen's achievement was remarkable for his time, as he completed these calculations by hand, without the aid of modern computers or calculators.

His dedication to the task led to a significant advancement in our understanding of pi.

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Answer:

y=2x+1

Step-by-step explanation:

You use the equation y=mx+b and substitute m for the slope/gradient. Then you use (2,5) to subtitue for y and x. Solve the equation for b. Then you have your slope and b, and you can make your equation from this.

1) First, from the picture we see that we have two equal angles: ∠A = ∠D = 47°.

2) Secondly, We also know that the line CF bisects AD.

3) Finally, the two opposite angles of B are equal, we call these angles ∠B.

From (1)-(2)-(3) we conclude that the answer is: angle-side-angle (ASA).

For example, we have the side/line AB between angles ∠A and ∠B.

Answer:

$7.50

Step-by-step explanation:

round 53.43 down to 50

tip = total cost * rate of tip

I hope this helped

A conclusion about the value of a population parameter based on information from the corresponding sample statistics and the associated the associated probability distributions.

Statistical inference is the process of making conclusions or inferences about the characteristics of a population based on information obtained from a sample.

It involves using statistical techniques to draw generalizations or estimates about population parameters using sample data.

A conclusion about the value of a population parameter based on information from the corresponding sample statistics and the associated the associated probability distributions.

Statistical inference involves two main components:

1. Estimation: Estimation involves using sample data to estimate or approximate the value of a population parameter.

2. Hypothesis Testing: Hypothesis testing is used to make decisions or draw conclusions about the population based on sample data.

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The product of a rational and an irrational number can be either rational or irrational, depending on the specific numbers involved.

To illustrate this, let's consider an example:

Let's say we have the rational number 2/3 and the irrational number √2.

Their product would be (2/3) * √2.

In this case, the product is irrational.

The square root of 2 is an irrational number, and when multiplied by a rational number, the result remains irrational.

However, it's also possible to have a product of a rational and an irrational number that is rational. For example, if we consider the rational number 1/2 and the irrational number √4, their product would be (1/2) * 2, which equals 1. In this case, the product is a rational number.

Therefore, we cannot make a definitive statement that the product of a rational and an irrational number is always rational or always irrational. It depends on the specific numbers involved in the multiplication.

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Dayna erases the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, and 11, and leaves only the integer 12 on the chalkboard, by the concept of multiplicative inverse and by using the extended Euclidean algorithm.

The integers from 1 through 6, as well as their multiplicative inverse \($\mod{13}$\), have been erased from the integers 1 through 12. We need to find the only integer that Dayna did not erase. We can find the multiplicative inverse of an integer a modulo 13 by using the extended Euclidean algorithm.

The integers from 1 through 6 are 1, 2, 3, 4, 5, and 6. We need to find their multiplicative inverses modulo 13.

The multiplicative inverse of 1 modulo 13 is 1, since

\($1 \times 1 \equiv 1 \pmod{13}$\).

The multiplicative inverse of 2 modulo 13 is 7, since

\($2 \times 7 \equiv 1 \pmod{13}$\).

The multiplicative inverse of 3 modulo 13 is 9, since

\($3 \times 9 \equiv 1 \pmod{13}$\).

The multiplicative inverse of 4 modulo 13 is 10, since

\($4 \times 10 \equiv 1 \pmod{13}$\).

The multiplicative inverse of 5 modulo 13 is 8, since

\($5 \times 8 \equiv 1 \pmod{13}$\).

The multiplicative inverse of 6 modulo 13 is 11, since

\($6 \times 11 \equiv 1 \pmod{13}$\).

Therefore, the only integer that Dayna does not erase is 12.

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The decimal equivalent of the hex number 0x3F is 63.

To convert the hex number 0x3F to its decimal equivalent, we need to multiply each digit by the corresponding power of 16 and sum them up.

Starting from the rightmost digit, we have:

Now, we multiply each digit by the corresponding power of 16:

Finally, we sum up the results:

(15 * 1) + (3 * 16) = 15 + 48 = 63

Therefore, the decimal equivalent of the hex number 0x3F is 63.

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The perimeter of the Christian's sandbox is 24 feet.

The given two quadrialterals are similar

Let us find the remaining lengths of Christian's sandbox

By proportional equation

36/8=18/x=27/y=18/z

4.5=18/x=27/y=18/z

x=18/4.5 = 4

y=27/4.5 = 6

z=4

The perimeter is sum of all the sides

So perimeter of Christian's sandbox is 8+6+4+4

24 feet

Hence, the perimeter of the Christian's sandbox is 24 feet.

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The algebraic rule for each kind of rotation is completed below and a 360° rotation would appear as if the shape didn't rotate at all.

As a general rule of rotation, the algebraic rule for each kind of rotation are

Rotation Algebraic rule

90° clockwise about the origin (x, y)→ (y, -x)

180° about the origin (x, y) → (-x, -y)

270° clockwise about the origin (x, y) → (-y, x)

The images of the triangles cannot be drawn because they are not given

A 360° rotation about the origin would result in the original shape returning to its starting position.

It would appear as if the shape didn't rotate at all.

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The Converse of the Angle Bisector Theorem states that if a point is in the same plane as an angle and divides the angle into two congruent angles, then it lies on the angle's bisector.

The fact that the converse states that the point must be in the same plane as the angle implies that if the point is not in the same plane as the angle, then it cannot divide the angle into two congruent angles, and thus cannot lie on the angle's bisector.

The Angle Bisector Theorem states that if a ray bisects an angle of a triangle, then it divides the opposite side into segments that are proportional to the other two sides of the triangle. The converse of this theorem states that if a point on the interior of a triangle divides one side of the triangle into two segments that are proportional to the other two sides, then the point lies on the bisector of the angle opposite the divided side.

To understand why this implies that the point must be in the same plane as the angle, we need to consider the definition of a plane. A plane is a flat, two-dimensional surface that extends infinitely in all directions.

It is determined by any three non-collinear points in space. In the context of a triangle, the three vertices of the triangle are non-collinear points that determine a plane.

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Therefore, the unique value of c for this case is 1/2, which does not depend on p.

The Mean Value Theorem is a fundamental result in calculus that relates

f(b) - f(a) = f'(c) (b - a).

by the question.

We have, f(x) = x², where p > 1 and [a, b] = [0, 1].

Then, f(a) = f(0) = 0 and f(b) = f(1) = 1.

Also, f'(x) = 2x.

Now, by the Mean Value Theorem, there exists at least one number c in (a, b) such that:

f(b) - f(a) = f'(c)(b-a)

Substituting the values, we get:

1 - 0 = f'(c)(1-0)

1 = 2c

c = 1/2

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There will be 6400000 bacteria in 96 hours.

Given the population of bacteria = 500

The population of the bacteria can multiply threefold in 12 hours. That means, after 12 hours the population of bacteria will be 500 * 3 = 1500.

At the end of 24 hours, the population of bacteria will be 1500 * 3 = 4500.

At the end of 36 hours, the population of bacteria will be 4500 * 3 = 13500.

Using the above formula, we can calculate the population of the bacteria at any given time.

Now, let's calculate the population of bacteria at the end of 96 hours

The population of bacteria = Initial population * (growth rate)^(time/interval)

Initial population = 500

Growth rate = 3

Interval = 12 hours

Time = 96 hours

Therefore, the Population of bacteria = 500 * (3)^(96/12) = 6400000

Hence, there will be 6400000 bacteria in 96 hours.

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Creating a discussion question, evaluating prospective solutions, and brainstorming and evaluating possible solutions are steps in problem-solving.

What is problem-solving?

Problem-solving is the method of examining, analyzing, and then resolving a difficult issue or situation to reach an effective solution.

Problem-solving usually requires identifying and defining a problem, considering alternative solutions, and picking the best option based on certain criteria.

Below are the steps in problem-solving:

Step 1: Define the Problem

Step 2: Identify the Root Cause of the Problem

Step 3: Develop Alternative Solutions

Step 4: Evaluate and Choose Solutions

Step 5: Implement the Chosen Solution

Step 6: Monitor Progress and Follow-up on the Solution.

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There is insufficient evidence to conclude that those with the high incomes are the ones that have the more credit scores.

We have the bar x = 705.9

The value of n = 34

mean = 724 . 1

standard deviation = 83.4

the level of significance = 5 percent level

The Hypothesis formulation

The null hypothesis H0 = u 705.9

alternative hypothesis = H1 u > 705.9

The t test is given as x - u / s /√n

= (724.1 - 705.9) / (83.4 / √34)

= 1.2725

The degree of freedom = 34 - 1 = 33

The test that we have here is a right tailed test

The p value for the test is given as probability of p (t33 > t)

= 0.1064

From the solution that we have here, we can see that the p value that has been calculated is greater than the level of significance.

Given that this is the case, the decision rule would be for us not to reject the null hypothesis.

There is insufficient evidence to the claim that the high income persons have the greater credit scores.

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Answer:

A' = (6, 3)

B' = (1, 1)

C' = (8, 7)

Step-by-step explanation:

Vertices of triangle ABC:

Given mapping rule:

(x, y) → (x + 4, y + 6)

This notation tells you that the x-coordinate is translated 4 units to the right, and the y-coordinate is translated 6 units up.

Substitute the coordinates of each point into the mapping rule to find the vertices of triangle A'B'C':

⇒ A' = (2 + 4, -3 + 6) = (6, 3)

⇒ B' = (-3 + 4, -5 + 6) = (1, 1)

⇒ C' = (4 + 4, 1 + 6) = (8, 7)

The equation of the ellipse with a major axis 24 units long parallel to the x-axis, a minor axis 22 units long, and a center at (6,1) can be written in the standard form.

The standard form of an ellipse with a major axis parallel to the x-axis is given by: ((x - h)^2 / a^2) + ((y - k)^2 / b^2) = 1. where (h, k) represents the center of the ellipse, and a and b represent half the lengths of the major and minor axes, respectively. In this case, the center is (6, 1), so h = 6 and k = 1. The major axis has a length of 24 units, so a = 24 / 2 = 12. The minor axis has a length of 22 units, so b = 22 / 2 = 11. Substituting these values into the standard form equation, we get: ((x - 6)^2 / 12^2) + ((y - 1)^2 / 11^2) = 1.

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Answer:

32.5 days. He already knows 10 leaving 65 words to learn. At 2 words a day divide and in 42m5 days he Wil be able to spell 75 words.

Answer:

-28/7

Step-by-step explanation:

First we need to make both denominators the same.

We can simplify the fraction on the left by dividing the top and bottom by 8.

This gives us;

⇒ \(\frac{1}{7}\)

To make the denominator of 4, 7 as well multiply 4 by 7;

⇒ \(\frac{28}{7}\)

Now this is easy as you can just subtract the numerators;

⇒ \(\frac{1}{7} - \frac{28}{7} = -\frac{27}{7}\)

Answer: 3/4 x 2/3 = 1/2 cups of sugar

Step-by-step explanation:

Answer:

that look like  complementry and supplementry angles

Step-by-step explanation:

Answer:

Hello!!! Princess Sakura here ^^

Step-by-step explanation:

<a & <h are alternate exterior angles because they're a pair of angles on the outer side of each of those two parallel lines but on opposite sides of the transversal.

Answer:

..........................

The gap between the highest and lowest values in a set of integers is known as the range in math for the sixth grade. You can use the steps below to determine the range:

What do the terms range and domain in a function example mean?

A straightforward function, such as f(x) = x^2, can have a domain (what goes in) of just the counting numbers 1, 2, 3, etc., and a range (what comes out) of the set 1, 4, 9, etc. Another function, g(x) = x^2, may have an integer domain of..., -3, -2, -1, 0... 1, 2, 3, and its range is..., 1, 4, 9,...

The set's numbers should be noted down.

In the set, identify the highest number. The set's highest value is this.

Identify the lowest value in the group. This is the set's minimal value.

To determine the range, deduct the smallest value from the greatest value.

Think about the group of numbers 2, 5, 8, 9, and 10, for instance.

The set has the digits 2, 5, 8, 9, and 10.

The top number is 10.

The bare minimum is two.

10 - 2 = 8 is the range.

The range of the set "2, 5, 8, 9, 10" is therefore 8.

The range of a function, or the set of all possible output values that the function can produce, may also be covered in sixth-grade math lessons. You can use algebraic methods to determine the potential values that a function can take in order to determine its range.

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Perimeter - The length of the east side of the garden is 50 feet.

What is perimeter?

A closed path that covers, encircles, or outlines a one-dimensional length or a two-dimensional shape is called a perimeter. A circle's or an ellipse's circumference is referred to as its perimeter. There are numerous uses in real life for perimeter calculations. The measurement of the fence needed to completely enclose a yard or garden is called the perimeter. How far a wheel or circle will roll in one revolution is determined by its circumference, or perimeter. Similar to this, the circumference of a spool is related to the length of string looped around it; if the string's length were correct, it would match the circumference.

The perimeter of the rectangle =280 (given)

let us assume the northside of the rectangle to be the length which is equal to 90feet (given) and east side of the garden be the breadth

Perimeter = 2(length+breadth)

280=2(90+breadth)

140=90+breadth

140-90=breadth

50feet = breadth

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Answer:

Assuming that a and b are not the hypotenuse then B would be equal to A, so B would equal 25m

Step-by-step explanation:

I hope this is right, you didn't put a picture.

The number from greatest to least in the given set of numbers are:

-14/5 < -2.25 < 1 ¼ < 3/2

A group of numbers is referred to as an element and makes up a set of numbers. The collection of numbers in the set may be infinite or finite. Roster notation is a method for indicating sets. For example, the set "2,31" contains the elements 2 and 31.

We need a way to say which numbers are included when a set has an infinite number of elements because it is impossible to list them all. Our number system is based on a few well-known infinite sets.

Given mixed fractions and decimals:

-14/5, -2.25, 1 ¼, 3/2

So,

-14/5 = −2.8

-2.25

1 ¼ = 1.25

3/2 = 1.5

As, −2.8 < -2.25 < 1.25 < 1.5, The numbers from greatest to least are:

-14/5 < -2.25 < 1 ¼ < 3/2.

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Complete question:

Answer:

Your answer is 105km travelled in 7 hours.

Step-by-step explanation:

Divide 150km by 10 to find the amount of km travelled in 1 hour. Then multiply that answer by 7.

Answer:

(1 , 0)

Step-by-step explanation:

On the x-axis, the value of y- coordinate is 0

The block reaches the bottom of the incline with a speed of approximately 7.66 m/s.

The acceleration of the block is given by

a = g sin 30 = 9.8 m/s² × 0.5 = 4.9 m/s²

Where g is the acceleration due to gravity.

The distance travelled by the block is given by

d = 3 m

The initial velocity of the block, u = 0

Using the kinematic equation, v² = u² + 2as

The final velocity of the block,v is given by

v = sqrt(2 × 4.9 × 3) ≈ 7.66 m/s

Therefore, the block reaches the bottom of the incline with a speed of approximately 7.66 m/s.

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